Posts Tagged mathematics

What do job-application aptitude tests actually measure?

What do aptitude tests measure?

What do aptitude tests measure?

This excellent essay, A Mathematician’s Lament, by Paul Lockhart has convinced me of something I suspected since learning actual mathematics at university (and not even, at first, within official lectures): our schooling ruins mathematics for children. The same kind of thinking that has created the education system appears to have infected human resource departments in most major companies. I refer, of course, to the ubiquitous use of aptitude tests (a subset of psychometric assessments).  It seems to me that our schools are satisfied with teaching arithmetic rather than mathematics and HR is satisfied with testing “skills” that no candidate will ever need. As with schooling it seems hardly anyone questions the current system. Read the rest of this entry »


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Don’t spot the pattern

If I write 2 then 4 then 6, then we feel good because we know that next comes 8. We can foresee it. We are not in the hands of destiny. Unfortunately, however, this has nothing to do with truth. – Arthur Seldom, The Oxford Murders (movie)

If you watched the movie The Oxford Murders then you’ll know of the futility of trying to guess the next number in a sequence. On my blog J delta rho I have placed a little rant about asking people to spot patterns. Here are the first few lines:

I remember getting questions at school of the form “which number comes next?” At the time I thought these questions were perfectly normal. I now think they are nonsensical. As such it troubles me to see similar questions (with diagrams rather than numbers) are being used in psychometric assessments.

Read more here.

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Mental arithmetic: a useless skill

How important is it to be able to do mental calculations? That’s in your head. I know that there are people that can work out crazy things like 12373 in their heads, but I am not one of those people. Why do companies still ask for candidates to perform mental calculations in job interviews or assessments?

I am a mathematician (that is, I have a masters degree in mathematics) and non-mathematicians often expect that I should be able to add up or divide the bill when we are in a restaurant. Then I need to explain that, actually, mathematics is not about numbers (I hardly ever see actual concrete numbers) and that I was probably going to make a mistake.

I get fluttered and nervous when I have to do mental arithmetic, particularly if other people are waiting for the answer. (I find dividing be three, or any other odd number, especially hard). The more real maths I have done, the more I have lost my ability to do calculations in my head. I consider concepts far more important. We have calculators and computers for a reason. I like to leave the calculations to those devices.

I have a distinct bias in expressing the above opinion, exactly because I am not good at mental calculations. I want to justify my inability to do such seemingly simple things. I want to prove that it is not important, that my other skills are far more valuable, that spending my time improving my mental calculation skills would be wasteful. Does it matter that my mental arithmetic is poor? Will I ever find myself in a (non-contrived) situation where it is actually important?

I was recently asked to do a simple calculation at a job interview and I could not get the right answer at first (in fact, I was so obviously wrong, that my interviewers may have doubted my credentials). Embarrassed, I got the correct answer later, when my mind had calmed down.

I failed a McKinsey entrance test which relied on being able to make mental approximations to a number of arithmetic problems in a very limited amount of time. Even though I understood most of the concepts involved, I could not perform these mental calculations at the required speed. I could have practiced such calculations for a month or two (or more) beforehand and (probably) have passed, but why? Hypothetically, some client might ask what the profit would be if x and y had certain values, but if the answer were important it would need to be arrived it far more elaborately and placed in some important document. In any case, I don’t particularly mind not having quick answers to such questions. I’d rather give you a thoroughly considered answer.

To me, mental calculations are a party-trick. It’s worthless unless you understand why you’re making the calculations and for any “important” work you’re going to be dealing with excel or computer models or in any case. I would rather spend my time improving my understanding of the concepts and how to use the computers that will do the number-crunching for me. In an age where computing power is cheap, but creativity paramount, this seems the right strategy.

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Some mathsy poetry

During a small group meeting not very long ago, I found myself having to be creative on the spot. I came up with a little poem riddled with maths references (and some other things – there is a religious element too). I would be interested in seeing how many of the references people get, so please post some comments.

coffee cups and donuts

somewhere, not too far to reach
orbits a teapot
the Pope cannot see it
monsters fly around it
telescopes search for it
and planets with four stars
bear gifts of coffee cups
and donuts; spheres knot
and cannot be untied,
the Primes march in a line
the universe is but Your shadow

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Being a mathematician in Amsterdam

I have been studying mathematics in Amsterdam for a nearly year now. I felt I needed to record my experiences of Amsterdam in story form. However, I have also wanted to write something about mathematics, about how mathematicians see mathematics, and why they do it, in a form that even non-mathematicians can understand. I tried to do both these things in a little story I wrote. It is heavily based on my own experiences in Amsterdam, of studying mathematics and of interacting with  mathematicians both in the Netherlands and in South Africa.

The story is divided into six lessons, each a snapshot of David’s life, where David’s thoughts, recollections and interactions with others give some insight (I hope) into the mind and life of a mathematician.  I have entitled it “The lives of the mathematicians.”

Here is  a link to the story. Let me know if you like (or if you hate it, or have any other kind of experience).

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